Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six

20 Oct 2020 · Zhengwei Liu, Sebastien Palcoux, Yunxiang Ren ·

This paper classifies the Grothendieck rings of complex fusion categories of multiplicity one up to rank six. Among 72 possible fusion rings, $25$ ones are filtered out by using categorification criteria. Each of the remaining 47 fusion rings admits a unitary complex categorification. We found 6 new Grothendieck rings, categorified by applying a localization approach of the Pentagon Equation.

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Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six

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